📚 Building Fraction Sense

WALT: We Are Learning To recognise, represent, compare and convert improper fractions and mixed numbers.

Success criteria:

• I can explain what the numerator and denominator tell me.

• I can represent a fraction greater than one using wholes and a number line.

• I can convert between improper fractions and mixed numbers.

• I can compare, order and simplify fractions, and explain my reasoning.

Worked examples

Example 1: In 7/4, the denominator 4 means each whole is divided into 4 equal parts. Seven quarters make one whole and three quarters, so 7/4 = 1 3/4.

Number-line thinking: 7/4 is one quarter before 2, so it lies between 1 and 2 at 1 3/4.

Example 2: To convert 11/5, divide 11 by 5. The quotient is 2 wholes and the remainder is 1, so 11/5 = 2 1/5. The denominator stays 5.

a) 8/3 = _________    b) 13/4 = _________    c) 9/2 = _________

a) 2/3 = ___/12    b) 3/5 = 12/___    c) 4/7 = ___/21

a) 12/18 = _________    b) 15/20 = _________    c) 21/28 = _________

Support: Use fraction strips or a number line. Remember: the denominator tells you how many equal parts make one whole. Use the sentence starter: “I made ___ whole(s) because…”.

✏️ Compare, Convert and Explain

a) 3/4 = ______ decimal = ______%

b) 0.6 = ______ fraction = ______%

c) 25% = ______ decimal = ______ fraction

5/6 ______ 7/9

________________________________________________________________________

a) Convert 14/5 to a mixed number: ____________________

b) Which is greater, 9/4 or 2? Explain why.

Challenge prompt: Place 17/6 and 23/8 on a number line. Which is greater? Can you create a fraction between them?

✅ Answer Key — Teacher Page

1. 5/3 = 1 2/3. It lies between 1 and 2, two thirds of the way from 1 to 2.

2. a) 2 2/3    b) 3 1/4    c) 4 1/2

3. a) 8/12    b) 20    c) 12/21

4. a) 2/3    b) 3/4    c) 3/4

5. a) 0.75, 75%    b) 3/5, 60%    c) 0.25, 1/4

6. 5/6 > 7/9. For example, using a common denominator: 5/6 = 15/18 and 7/9 = 14/18.

7. 3/4, 5/6, 7/6, 1 1/5.

8. 9/4 = 2 1/4, so Mia has walked more than 2 kilometres.

9. Answers vary. Example: 9/4 = 2 1/4, which is greater than 2 and less than 2 1/2.

10. a) 14/5 = 2 4/5.    b) 9/4 = 2 1/4, so 9/4 is greater than 2.

Extension: 17/6 = 2 5/6 and 23/8 = 2 7/8, so 23/8 is greater. Answers for a fraction between them may vary.